Introduction to Functional Programming
... lambda calculus. It is widely agreed that languages such as Haskell and Miranda are
purely functional, while SML and Scheme are not. However, there are some small
differences of opinion about the precise technical motivation for this distinction. Scheme
and Standard ML are predominantly functional ...
Functional Programming in Haskell
... Functional vs. Imperative Programming
The program specifies what the computer should do.
The program specifies what the value of a function should be.
The exact sequence of steps to compute this value is left unspecified.
This is one form of declarati ...
... F(n) = n * F(n-1) for n > 0
F(0) = 1
Lazy evaluation - Computer Science and Engineering
... request for some output from another function
requiring some input.
• Therefore, the functions call each other and
returns values as and when required.
• For example, in tree equality, if first value of both
the trees in preorder sequence are equal then
second element of first tree is computed follo ...
Functional Programming in Scheme
... dynamically typed language or, equivalently, latent typed. In a latent typed language, types
are associated to values rather than to the program identifiers and the type checking is
performed at run time. Also Scheme is sometimes considered as a weak-typed language
since values of any type can be mi ...
... letrec in Scheme
• letrec – all the bindings are in effect while
their initial values are being computed,
allows mutually recursive definitions
(if (zero? n)
(odd? (- n 1)))))
(if (zero? n)
(even? (- n 1))))))
... Introduction to FP
Imperative programming vs. functional
Language applied to functional programming is
LISP – LISt Programming.
It was invented to provide language features for list
processing, the need for which grew out of the
first application in the area of AI, expert systems,
C# is a functional programming language
... The CLR has direct support for many of the features
◦ Delegates are special classes with fast calling convention
◦ Generics (parametric polymorphism) is implemented by just-intime specialization so no boxing is required
◦ Closure conversion is done by the C# compiler, which shares
ppt - Dave Reed
... each call to add keeps the vector sorted
each call to addFast is O(1), but means the vector may not be sorted
IsStored first checks the data field: if !isSorted, then call MergeSort first
Closure and Environment
... Nested HOL is a key feature in modern
functional programming languages
And now has grown into other language
Pretty Printing with Lazy Dequeues
... For our first implementation of the token interpreter we do not yet care about
boundedness. So the interpreter decides if a group is formatted horizontally or
vertically only after it has been traversed, that is, the decision is made at the Close
token of the group. An implementation that makes the ...
X - Rensselaer Polytechnic Institute: Computer Science
... • Embedding is when procedure values are put in data
• Embedding has many uses:
– Modules: a module is a record that groups together a set of related
– Software components: a software component is a generic function
that takes a set of modules as its arguments and returns a new ...
... nonlocal references are resolved at the point of
Static scoping is implemented by associating a
closure (instruction pointer and environment
pointer) with each function as it is defined.
The run-time execution stack maintains static
links for nonlocal references.
Top-level defin ...
Class Notes 2b: Scheme Reference
... • It correctly treats functional arguments,
thanks to lexical scoping.
– Functions are first-class objects: they
can be created, assigned to variables,
passed as arguments, returned as values.
... • In reality, both pointers to A point to the SAME symbol (i.e., the
same exact mem location)
• EQ: tests for memory location exactly, therefore, atoms only!
• LISP automatically makes sure that all refs to some symbol
actually point to the UNIQUE point in mem that the symbol
happens to be stored ph ...
19. Introduction to evaluation order
... Different evaluation orders give different 'results'
• The number 1
• A non-terminating calculation
Two different semantics of function application are involved:
• Strict: A function call is well-defined if and only if all actual parameters are
• Non-strict: A function call can be well- ...
Foundations of Functional Programming
... 5. Its notions of confluence (Church-Rosser property), termination, and normal form apply generally in rewriting theory.
6. Lisp, one of the first major programming languages, was inspired by the
λ-calculus. Many functional languages, such as ML, consist of little more
than the λ-calculus with addit ...
Downloadable PowerPoint file
... efficient as iteration
This is always possible in the face of
tail recursion, where the recursive
call is the last operation before
Cryptography - Mathematical Association
... There are a few things to note about this definition.
If the value of a is 0 or b2 – 4ac < 0 then an error is raised. The appropriate error comment will be
printed on screen.
otherwise is used to catch any values that do not satisfy any of the other clauses – we could have
used this in the last ...
Lambda Calculus as a Programming Language
... "theoretically" we should. We forbid the use of the symbol as a free variable within the λexpression itself. This is in line with Lambda calculus where λ-expressions must be
textually finite and where free variables have nothing to do with defining recursive
The notation E1 = E2 is used t ...
... Definition From the "comp.lang.functional FAQ"
Functional programming is a style of programming that
emphasizes the evaluation of expressions, rather than
execution of commands. The expressions in these
language are formed by using functions to combine
basic values. A functional language is a langua ...
... of the results of applying the function to
elements taken from each list
> (map abs '(3 -4 2 -5 -6))
In computer science, a tail call is a subroutine call performed as the final action of a procedure. If a tail call might lead to the same subroutine being called again later in the call chain, the subroutine is said to be tail-recursive, which is a special case of recursion. Tail recursion (or tail-end recursion) is particularly useful, and often easy to handle in implementations.Tail calls can be implemented without adding a new stack frame to the call stack. Most of the frame of the current procedure is not needed any more, and it can be replaced by the frame of the tail call, modified as appropriate (similar to overlay for processes, but for function calls). The program can then jump to the called subroutine. Producing such code instead of a standard call sequence is called tail call elimination. Tail call elimination allows procedure calls in tail position to be implemented as efficiently as goto statements, thus allowing efficient structured programming. In the words of Guy L. Steele, ""in general procedure calls may be usefully thought of as GOTO statements which also pass parameters, and can be uniformly coded as [machine code] JUMP instructions.""Traditionally, tail call elimination is optional. However, in functional programming languages, tail call elimination is often guaranteed by the language standard, and this guarantee allows using recursion, in particular tail recursion, in place of loops. In such cases, it is not correct (though it may be customary) to refer to it as an optimization. The special case of tail recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls.